Inhomogeneous charged black hole solutions in asymptotically anti-de Sitter spacetime

TL;DR

This work analyzes static inhomogeneous charged planar black holes in four-dimensional Einstein-Maxwell theory with AdS asymptotics by linear perturbations around the RN-AdS background. Analytically in the long-wavelength limit and numerically across wavelengths, it shows that the Cauchy horizon generically dissolves into a curvature singularity for non-extremal solutions, while extremal solutions develop a pp curvature singularity at the horizon for long-wavelength perturbations, producing infinite tidal forces despite a small Kretschmann scalar. These findings reinforce strong cosmic censorship in AdS settings and illuminate interior geometry consistent with Schwarzschild-AdS-like structures rather than RN-AdS inner horizons. The study also connects to holographic duals with periodic boundary potentials, providing a boundary force-balance perspective and highlighting potential quantum-corrections considerations for extremal cases.

Abstract

We investigate static inhomogeneous charged planar black hole solutions of the Einstein-Maxwell system in an asymptotically anti-de Sitter spacetime. Within the framework of linear perturbations, the solutions are numerically and analytically constructed from the Reissner-Nordström-AdS black hole solution. The perturbation analysis predicts that the Cauchy horizon always disappears for any wavelength perturbation, supporting the strong cosmic censorship conjecture. For extremal black holes, we analytically show that an observer freely falling into the black hole feels infinite tidal force at the horizon for any long wavelength perturbation, even though the Kretschmann scalar curvature invariant remains small.

Figures (8)

• Figure 1: (color online) $D=b(u)$ (solid curve), $F(u)$ (dashed curve), and $B_t(u)\times 10^{-1}$ (dotted curve) are shown, respectively for $\xi=0.5$, $q=3$.
• Figure 2: (color online) $D=b(u)$ (solid curve), $F(u)$ (dashed curve), and $B_t(u)\times 10^{-1}$ (dotted curve) are shown, respectively for $\xi=q=0.5$.
• Figure 3: (color online) $D=F(u)$ (solid curve) and $L^4 {\mathcal{K}}_1(u)\times 10^{-3}$ (dashed curve) are shown, respectively for $\xi=0.5$, $q=3$.
• Figure 4: (color online) $D=F(u)$ (solid curve) and $L^4 {\mathcal{K}}_1(u)\times 10^{-3}$ (dashed curve) are shown, respectively for $\xi=q=0.5$.
• Figure 5: (color online) $D=b(u)$ (solid curve), $F(u)$ (dashed curve), and $B_t(u)/10^2$ (dotted curve) are shown, respectively for $q=3$.